Supersymmetric Cold Dark Matter with Yukawa Unification

TL;DR

The paper investigates the neutralino relic density within an MSSM framework that enforces gauge and Yukawa coupling unification under gravity-mediated, universal boundary conditions. It advances a comprehensive calculation of annihilation and coannihilation processes, including a wide set of diagrams in the large $\tan\beta$ regime, and solves the Boltzmann equation with an effective cross section $\hat{\sigma}_{eff}$ to determine $\Omega_{LSP} h^2$. The results show the LSP is predominantly bino-like and that coannihilation with the nearly degenerate lightest stau NLSP is crucial to achieving relic densities in the cosmologically allowed range $0.09\le\Omega_{LSP} h^2\le0.22$, constraining the mass spectrum to $m_{\tilde{\chi}}\in [222,354]\,\text{GeV}$ and $m_{\tilde{\tau}_2}\in [232,369]\,\text{GeV}$ with $m_A$ between $95$ and $216$ GeV. These findings tightly restrict the MSSM Yukawa-unified parameter space and yield concrete, testable predictions for collider and dark matter phenomenology around the 200–400 GeV scale.

Abstract

The cosmological relic density of the lightest supersymmetric particle of the minimal supersymmetric standard model is calculated under the assumption of gauge and Yukawa coupling unification. We employ radiative electroweak breaking with universal boundary conditions from gravity-mediated supersymmetry breaking. Coannihilation of the lightest supersymmetric particle, which turns out to be an almost pure bino, with the next-to-lightest supersymmetric particle (the lightest stau) is crucial for reducing its relic density to an acceptable level. Agreement with the mixed or the pure cold (in the presence of a nonzero cosmological constant) dark matter scenarios for large scale structure formation in the universe requires that the lightest stau mass is about 2-8% larger than the bino mass, which can be as low as 222 GeV. The smallest allowed value of the lightest stau mass turns out to be about 232 GeV.

Figures (5)

• Figure 1: The mass parameters $m_0$ and $M_{1/2}$ as functions of $m_A$ for $\Delta_{\tilde{\tau}_2}=0.02$ (solid lines) and 0.08 (dashed lines).
• Figure 2: The relevant part of the sparticle spectrum as a function of $m_A$ for $\Delta_{\tilde{\tau}_2}= 0.047$. The LSP mass, for $\Delta_{\tilde{\tau}_2}= 0.02$, is also included (dashed line).
• Figure 3: The LSP abundance $\Omega_{LSP}~h^2$ as a function of $m_A$ for $\Delta_{\tilde{\tau}_2}=0$, 0.02, 0.047 and 0.08 as indicated. The limiting lines at $\Omega_{LSP}~h^2=0.09$ and 0.22 are also included.
• Figure 4: The cosmologically allowed region in the $m_A-\Delta_{\tilde{\tau}_2}$ plane, where $\Omega_{LSP}~h^2$ lies in the range $0.09-0.22$. We also take $m_A\geq 95$ GeV and $M_{1/2}\leq 800$ GeV.
• Figure 5: The relative contributions $\hat{\sigma}_{(\tilde{\chi}\tilde{\chi})}/\hat{\sigma}_{eff}$ (solid line), $\hat{\sigma}_{(\tilde{\chi}\tilde{\tau}_2)} /\hat{\sigma}_{eff}$ (dashed line) and $\hat{\sigma}_{(\tilde{\tau}_2\tilde{\tau}_2^{(\ast)})}/ \hat{\sigma}_{eff}$ (dot-dashed line) of the three inclusive (co)annihilation reactions to $\hat{\sigma}_{eff}$ as functions of $m_A$ for $\Delta_{\tilde{\tau}_2}=0.047$.